OFFSET
0,4
COMMENTS
a(n) is also the number of ways to tile a 1 X n strip with squares, four colors of trominos, and 2 colors of pentominos.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,4,0,2).
FORMULA
a(n) = a(n-1) + 4*a(n-3) + 2*a(n-5).
Sum_{k=0..n} a(k) = (a(n+5) - 4*a(n+2) - 4*a(n+1) - 1)/6.
G.f.: -1/(2*x^5+4*x^3+x-1).
EXAMPLE
Here is a demonstration that a(3) = 5.
._____. ._____. ._____. ._____. ._____.
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MATHEMATICA
LinearRecurrence[{1, 0, 4, 0, 2}, {1, 1, 1, 5, 9}, 40];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Drisana Bhatia and Greg Dresden, Jun 29 2021
STATUS
approved